Lecture 12 - Internal Flow General Considerations and...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Internal Flow: General Considerations and Correlations Lecture 12 - Chapter 8 Dr. Srinath Ekkad
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Entrance Conditions Entrance Conditions Must distinguish between entrance and fully developed regions . Hydrodynamic Effects : Assume laminar flow with uniform velocity profile at inlet of a circular tube . Velocity boundary layer develops on surface of tube and thickens with increasing x . Inviscid region of uniform velocity shrinks as boundary layer grows. Does the centerline velocity change with increasing x ? If so, how does it change? Subsequent to boundary layer merger at the centerline, the velocity profile becomes parabolic and invariant with x . The flow is then said to be hydrodynamically fully developed . How would the fully developed velocity profile differ for turbulent flow?
Background image of page 2
Entrance Conditions (cont) Thermal Effects : Assume laminar flow with uniform temperature, , at inlet of circular tube with uniform surface temperature , , or heat flux , . ( 29 ,0 i T r T = s i T T s q Thermal boundary layer develops on surface of tube and thickens with increasing x . Isothermal core shrinks as boundary layer grows. Subsequent to boundary layer merger, dimensionless forms of the temperature profile become independent of x . ( 29 for and s s T q Conditions are then said to be thermally fully developed . Is the temperature profile invariant with x in the fully developed region?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Entrance Conditions (cont) For uniform surface temperature, what may be said about the change in the temperature profile with increasing x ? For uniform surface heat flux, what may be said about the change in the temperature profile with increasing x ? How do temperature profiles differ for laminar and turbulent flow?
Background image of page 4
Mean Quantities The Mean Velocity and Temperature Absence of well-defined free stream conditions, as in external flow, and hence a reference velocity or temperature , dictates the use of a cross- sectional mean velocity and temperature for internal flow. ( 29 u ( 29 T ( 29 m u ( 29 m T ( 29 or, , c A c m u r x dA ρ = g ( 29 Hence, , c A c m c u r x dA u A = o r For incompressible flow in a circular tube of radius , ( 29 0 2 2 , o r m o u u r x r dr r = Linkage of mean velocity to mass flow rate : m c m u A = g
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Mean Quantities (cont) Linkage of mean temperature to thermal energy transport associated with flow through a cross section: c t A p c p m E uc T dA mc T ρ = g g Hence, n = c A p c m p uc T dA T mc g For incompressible , constant-property
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 23

Lecture 12 - Internal Flow General Considerations and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online